Problem: If $m \angle AOC = 180^\circ$ and $m \angle AOB = 23^\circ$, what is $m \angle BOC$, in degrees? $23^\circ$ $O$ $A$ $C$ $B$
Solution: From the diagram, we see that $\angle AOB$ and $\angle BOC$ are supplementary angles. Therefore, $m \angle AOB + m \angle BOC = 180^\circ$ Thus, $m \angle BOC = 180^\circ - m \angle AOB = 180^\circ - 23^\circ = 157^\circ$.